1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various countries \(m\) of the world. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodolgy and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was 687710471b373ff5d19f908e5acb0fc83984dc1d.

2 Data

Data are downloaded from [3]. Minor formatting is applied to get the data ready for further processing.

3 Basic Exploration

Below we plot cumulative case count on a log scale by continent. Note that “Other” relates to ships.

Reported Cases by Continent

Reported Cases by Continent

Below we plot the cumulative deaths by country on a log scale:

Reported Deaths by Continent

Reported Deaths by Continent

4 Method & Assumptions

The methodology is described in detail here. We filter out countries with populations of greater than 500 000. Weeks where the deaths or cases are not greater than 50 are left out of results.

5 Results

5.1 Current \(R_{t,m}\) estimates by country

Below current (last weekly) \(R_{t,m}\) estimates are plotted on a world map.

5.1.0.1 Cases

5.1.1 Deaths

5.2 Top 10 countries

Below we show various extremes of \(R_{t,m}\) where counts (deaths or cases) exceed 50 in the last week.

5.2.1 Lowest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Israel deaths 91 2020-11-11 0.6 0.7 0.9
Oman deaths 52 2020-11-11 0.6 0.8 1.0
Paraguay deaths 75 2020-11-11 0.6 0.8 1.0
Bolivia deaths 57 2020-11-11 0.6 0.8 1.0
Moldova deaths 92 2020-11-11 0.7 0.9 1.0
Brazil deaths 1,901 2020-11-11 0.8 0.9 1.0
South_Africa deaths 412 2020-11-11 0.8 0.9 1.0
Chile deaths 292 2020-11-11 0.8 0.9 1.0
Bangladesh deaths 125 2020-11-11 0.8 0.9 1.1
Libya deaths 64 2020-11-11 0.7 0.9 1.2

5.2.2 Lowest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Cote_dIvoire cases 82 2020-11-11 0.3 0.4 0.6
Belgium cases 30,284 2020-11-11 0.5 0.5 0.6
Honduras cases 2,116 2020-11-11 0.5 0.6 0.7
Madagascar cases 112 2020-11-11 0.5 0.6 0.8
Guinea cases 271 2020-11-11 0.5 0.6 0.7
Jamaica cases 277 2020-11-11 0.6 0.6 0.7
Ireland cases 2,841 2020-11-11 0.6 0.7 0.7
Mozambique cases 621 2020-11-11 0.7 0.7 0.8
Netherlands cases 43,467 2020-11-11 0.7 0.7 0.8
El_Salvador cases 1,130 2020-11-11 0.7 0.7 0.8

5.2.3 Highest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Sudan deaths 279 2020-11-11 3.6 78.4 679.2
Greece deaths 211 2020-11-11 1.8 2.3 2.7
Slovakia deaths 155 2020-11-11 1.4 1.7 2.0
Switzerland deaths 479 2020-11-11 1.4 1.6 1.8
Bulgaria deaths 439 2020-11-11 1.4 1.6 1.7
Kosovo deaths 68 2020-11-11 1.2 1.5 1.9
Serbia deaths 71 2020-11-11 1.2 1.5 1.8
Italy deaths 2,918 2020-11-11 1.3 1.4 1.6
France deaths 3,918 2020-11-11 1.4 1.4 1.5
Bosnia_and_Herzegovina deaths 312 2020-11-11 1.3 1.4 1.6

5.2.4 Highest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Lesotho cases 65 2020-11-11 2.9 3.9 5.0
Sudan cases 289 2020-11-11 1.7 2.0 2.4
Zimbabwe cases 200 2020-11-11 1.5 1.8 2.1
Cameroon cases 318 2020-11-11 1.4 1.8 2.1
Algeria cases 4,467 2020-11-11 1.4 1.5 1.7
Estonia cases 1,251 2020-11-11 1.3 1.4 1.6
Djibouti cases 58 2020-11-11 1.1 1.4 1.8
Somalia cases 72 2020-11-11 1.2 1.4 1.6
Lithuania cases 9,388 2020-11-11 1.3 1.4 1.5
Ghana cases 1,102 2020-11-11 1.3 1.4 1.5

5.3 Country Plots by Continent

Below we plot results for each country/province in a list. We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds five.

5.3.1 Africa

5.3.1.1 Algeria

5.3.1.2 Angola

5.3.1.3 Benin

5.3.1.4 Botswana

5.3.1.5 Burkina_Faso

5.3.1.6 Burundi

5.3.1.7 Cameroon

5.3.1.8 Cape_Verde

5.3.1.9 Central_African_Republic

5.3.1.10 Chad

5.3.1.11 Comoros

5.3.1.12 Congo

5.3.1.13 Cote_dIvoire

5.3.1.14 Democratic_Republic_of_the_Congo

5.3.1.15 Djibouti

5.3.1.16 Egypt

5.3.1.17 Equatorial_Guinea

5.3.1.18 Eritrea

5.3.1.19 Eswatini

5.3.1.20 Ethiopia

5.3.1.21 Gabon

5.3.1.22 Gambia

5.3.1.23 Ghana

5.3.1.24 Guinea

5.3.1.25 Guinea_Bissau

5.3.1.26 Kenya

5.3.1.27 Lesotho

5.3.1.28 Liberia

5.3.1.29 Libya

5.3.1.30 Madagascar

5.3.1.31 Malawi

5.3.1.32 Mali

5.3.1.33 Mauritania

5.3.1.34 Mauritius

5.3.1.35 Morocco

5.3.1.36 Mozambique

5.3.1.37 Namibia

5.3.1.38 Niger

5.3.1.39 Nigeria

5.3.1.40 Rwanda

5.3.1.41 Senegal

5.3.1.42 Sierra_Leone

5.3.1.43 Somalia

5.3.1.44 South_Africa

5.3.1.45 South_Sudan

5.3.1.46 Sudan

5.3.1.47 Togo

5.3.1.48 Tunisia

5.3.1.49 Uganda

5.3.1.50 United_Republic_of_Tanzania

5.3.1.51 Western_Sahara

5.3.1.52 Zambia

5.3.1.53 Zimbabwe

5.3.2 America

5.3.2.1 Argentina

5.3.2.2 Bolivia

5.3.2.3 Brazil

5.3.2.4 Canada

5.3.2.5 Chile

5.3.2.6 Colombia

5.3.2.7 Costa_Rica

5.3.2.8 Cuba

5.3.2.9 Dominican_Republic

5.3.2.10 Ecuador

5.3.2.11 El_Salvador

5.3.2.12 Guatemala

5.3.2.13 Guyana

5.3.2.14 Haiti

5.3.2.15 Honduras

5.3.2.16 Jamaica

5.3.2.17 Mexico

5.3.2.18 Nicaragua

5.3.2.19 Panama

5.3.2.20 Paraguay

5.3.2.21 Peru

5.3.2.22 Puerto_Rico

5.3.2.23 Suriname

5.3.2.24 Trinidad_and_Tobago

5.3.2.25 United_States_of_America

5.3.2.26 Uruguay

5.3.2.27 Venezuela

5.3.3 Asia

5.3.3.1 Afghanistan

5.3.3.2 Bahrain

5.3.3.3 Bangladesh

5.3.3.4 Bhutan

5.3.3.5 China

5.3.3.6 India

5.3.3.7 Indonesia

5.3.3.8 Iran

5.3.3.9 Iraq

5.3.3.10 Israel

5.3.3.11 Japan

5.3.3.12 Jordan

5.3.3.13 Kazakhstan

5.3.3.14 Kuwait

5.3.3.15 Kyrgyzstan

5.3.3.16 Lebanon

5.3.3.17 Malaysia

5.3.3.18 Maldives

5.3.3.19 Myanmar

5.3.3.20 Nepal

5.3.3.21 Oman

5.3.3.22 Pakistan

5.3.3.23 Palestine

5.3.3.24 Philippines

5.3.3.25 Qatar

5.3.3.26 Saudi_Arabia

5.3.3.27 Singapore

5.3.3.28 South_Korea

5.3.3.29 Sri_Lanka

5.3.3.30 Syria

5.3.3.31 Taiwan

5.3.3.32 Tajikistan

5.3.3.33 Thailand

5.3.3.34 Turkey

5.3.3.35 United_Arab_Emirates

5.3.3.36 Uzbekistan

5.3.3.37 Vietnam

5.3.3.38 Yemen

5.3.4 Europe

5.3.4.1 Albania

5.3.4.2 Armenia

5.3.4.3 Austria

5.3.4.4 Azerbaijan

5.3.4.5 Belarus

5.3.4.6 Belgium

5.3.4.7 Bosnia_and_Herzegovina

5.3.4.8 Bulgaria

5.3.4.9 Croatia

5.3.4.10 Cyprus

5.3.4.11 Czechia

5.3.4.12 Denmark

5.3.4.13 Estonia

5.3.4.14 Finland

5.3.4.15 France

5.3.4.16 Georgia

5.3.4.17 Germany

5.3.4.18 Greece

5.3.4.19 Hungary

5.3.4.20 Ireland

5.3.4.21 Italy

5.3.4.22 Kosovo

5.3.4.23 Latvia

5.3.4.24 Lithuania

5.3.4.25 Luxembourg

5.3.4.26 Moldova

5.3.4.27 Montenegro

5.3.4.28 Netherlands

5.3.4.29 North_Macedonia

5.3.4.30 Norway

5.3.4.31 Poland

5.3.4.32 Portugal

5.3.4.33 Romania

5.3.4.34 Russia

5.3.4.35 Serbia

5.3.4.36 Slovakia

5.3.4.37 Slovenia

5.3.4.38 Spain

5.3.4.39 Sweden

5.3.4.40 Switzerland

5.3.4.41 Ukraine

5.3.4.42 United_Kingdom

5.3.5 Oceania

5.3.5.1 Australia

5.3.5.2 New_Zealand

5.3.5.3 Papua_New_Guinea

## Detailed Output

Detailed output for all countries are saved to a comma-separated value file. The file can be found here.

6 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

7 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim

[3] European Centre for Disease Prevention and Control, “Data on the geographic distribution of COVID-19 cases worldwide.” European Union, 2020 [Online]. Available: https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide